1. Field of the Invention
The present invention relates to atomic force microscopes (AFMs) and, more particularly, to an AFM and method of use thereof that dynamically controls the oscillating drive signal to the cantilever based on the amplitude of the measured response of the cantilever.
2. Description of the Related Art
An Atomic Force Microscope (“AFM”), as described in U.S. Pat. No. RE 34,489 to Hansma et al. (“Hansma”), is a type of scanning probe microscope (“SPM”). AFMs are high-resolution surface measuring instruments. Two general types of AFMs include contact mode (also known as repulsive mode) AFMs, and cyclical mode AFMs (periodically referred to herein as TappingMode™ AFMs.)
The contact mode AFM is described in detail in Hansma. Generally, the contact mode AFM is characterized by a probe having a bendable cantilever and a tip. The AFM operates by placing the tip directly on a sample surface and then scanning the surface laterally. When scanning, the cantilever bends in response to sample surface height variations, which are then monitored by an AFM deflection detection system to map the sample surface. The deflection detection system of such contact mode AFMs is typically an optical beam system, as described in Hansma.
Typically, the height of the fixed end of the cantilever relative to the sample surface is adjusted with feedback signals that operate to maintain a predetermined amount of cantilever bending during lateral scanning. This predetermined amount of cantilever bending has a desired value, called the setpoint. Typically, a reference signal for producing the setpoint amount of cantilever bending is applied to one input of a feedback loop. By applying the feedback signals generated by the feedback loop to an actuator within the system, and therefore adjusting the relative height between the cantilever and the sample, cantilever deflection can be kept constant at the setpoint value. By plotting the adjustment amount (as obtained by monitoring the feedback signals applied to maintain cantilever bending at the setpoint value) versus lateral position of the cantilever tip, a map of the sample surface can be created.
The second general category of AFMs, i.e., cyclical mode or TappingMode™ AFMs, utilize oscillation of a cantilever to, among other things, reduce the forces exerted on a sample during scanning. In contrast to contact mode AFMs, the probe tip in cyclical mode makes contact with the sample surface or otherwise interacts with it only intermittently as the tip is scanned across the surface. Cyclical mode AFMs are described in U.S. Pat. Nos. 5,226,801, 5,412,980 and 5,415,027 by Elings et al.
In U.S. Pat. No. 5,412,980, a cyclical mode AFM is disclosed in which a probe is oscillated at or near a resonant frequency of the cantilever. When imaging in cyclical mode, there is a desired tip oscillation amplitude associated with the particular cantilever used, similar to the desired amount of cantilever deflection in contact mode. This desired amplitude of cantilever oscillation is typically kept constant at a desired setpoint value. In operation, this is accomplished through the use of a feedback loop having a setpoint input for receiving a signal corresponding to the desired amplitude of oscillation. The feedback circuit servos the vertical position of either the cantilever mount or the sample by applying a feedback control signal to a Z actuator so as to cause the probe to follow the topography of the sample surface.
Typically, the tip's oscillation amplitude is set to be greater than 20 nm peak-to-peak to maintain the energy in the cantilever arm at a much higher value than the energy that the cantilever loses in each cycle by striking or otherwise interacting with the sample surface. This provides the added benefit of preventing the probe tip from sticking to the sample surface. Ultimately, to obtain sample height data, cyclical mode AFMs monitor the Z actuator feedback control signal that is produced to maintain the established setpoint. A detected change in the oscillation amplitude of the tip and a resulting feedback control signal are indicative of a particular surface topography characteristic. By plotting these changes versus the lateral position of the cantilever, a map of the surface of the sample can be generated.
Notably, AFMs have become accepted as a useful metrology tool in manufacturing environments in the integrated circuit and data storage industries. A limiting factor to the more extensive use of the AFM is the limited throughput per machine due to the slow imaging rates of AFMs relative to competing technologies. Although it is often desirable to use an AFM to measure surface topography of a sample, the speed of the AFM is typically far too slow for production applications. For instance, in most cases, AFM technology requires numerous machines to keep pace with typical production rates. As a result, using AFM technology for surface measurement typically yields a system that has a high cost per measurement. A number of factors are responsible for these drawbacks associated with AFM technology, and they are discussed generally below.
AFM imaging, in essence, typically is a mechanical measurement of the surface topography of a sample such that the bandwidth limits of the measurement are mechanical ones. An image is constructed from a raster scan of the probe over the area to be imaged. In both contact and cyclical mode, the tip of the probe is caused to scan across the sample surface at a velocity equal to the product of the scan size and the scan frequency. As discussed previously, the height of the fixed end of the cantilever relative to the sample surface can be adjusted during scanning at a rate typically much greater than the scanning rate in order to maintain a constant force (contact mode) or oscillation amplitude (cyclical mode) relative to the sample surface.
Notably, the bandwidth requirement for a particular application of a selected cantilever is generally predetermined. Therefore, keeping in mind that the bandwidth of the height adjustment (hereinafter referred to as the Z axis or Z-position bandwidth) is dependent upon the tip velocity as well as the sample topography, the required Z-position bandwidth typically limits the maximum scan rate for a given sample topography.
Further, the bandwidth of the AFM in these feedback systems is usually lower than the open loop bandwidth of any one component of the system. In particular, as the 3 dB roll-off frequency of any component is approached, the phase of the response is retarded significantly before any loss in amplitude response. The frequency at which the total phase lag of all the components in the system is large enough for the loop to be unstable is the ultimate bandwidth limit of the loop. When designing an AFM, although the component of the loop which exhibits the lowest response bandwidth typically demands the focus of design improvements, reducing the phase lag in any part of the loop will typically increase the bandwidth of the AFM as a whole.
With particular reference to the contact mode AFM, the bandwidth of the cantilever deflection detection apparatus is limited by a mechanical resonance of the cantilever due to the tip's interaction with the sample. This bandwidth increases with the stiffness of the cantilever. Notably, this stiffness can be made high enough such that the mechanical resonance of the cantilever is not a limiting factor on the bandwidth of the deflection detection apparatus, even though sensitivity to increased imaging forces may be compromised.
Nevertheless, in contact mode, the Z position actuator still limits the Z-position bandwidth. Notably, Z position actuators for AFMs are typically piezo-tube or piezo-stack actuators which are selected for their large dynamic range and high sensitivity. Such devices generally have a mechanical resonance far below that of the AFM cantilever brought in contact with the sample, typically around 1 kHz, thus limiting the Z-position bandwidth.
Manalis et al. (Manalis, Minne, and Quate, “Atomic force microscopy for high speed imaging using cantilevers with an integrated actuator and sensor,” Appl. Phys. Lett., 68 (6) 871–3 (1996)) demonstrated that contact mode imaging can be accelerated by incorporating the Z position actuator into the cantilever beam. A piezoelectric film such as ZnO was deposited on the tip-side of the cantilever. The film causes the cantilever to act as a bimorph such that by applying a voltage dependent stress, the cantilever will bend. This bending of the cantilever, through an angle of one degree, or even less, results in microns of Z positioning range. Further, implementing the Z position actuator in the cantilever increases the Z-position bandwidth of the contact mode AFM by more than an order of magnitude.
Nevertheless, such an AFM exhibits new problems with the Z positioning which were not concerns with other known AFMs. For instance, the range of the Z actuator integrated with the cantilever is less than is required for imaging many AFM samples. In addition, because the positioning sensitivity of each cantilever is different, the AFM requires recalibration whenever the probe is changed due to a worn or broken tip. Further, the sensitivity in some cases exhibits undesirable non-linearity at low frequencies. These problems can make the Z actuator integrated with the cantilever a less than optimal choice for general use as the Z actuator in commercial AFMs.
Furthermore, notwithstanding the above, in many AFM imaging applications, the use of contact mode operation is unacceptable. Friction between the tip and the sample surface can damage imaged areas as well as degrade the tip's sharpness. Therefore, for many of the applications contemplated by the present invention, the preferred mode of operation is cyclical mode, i.e., TappingMode™. However, the bandwidth limitations associated with cyclical mode detection are typically far greater than those associated with contact mode operation.
In cyclical or non-continuous contact mode operation, the AFM cantilever is caused to act as a resonant beam in steady state oscillation. When a force is applied to the cantilever, the force can be measured as a change in either the oscillation amplitude or frequency. One potential problem associated with cyclical mode operation is that the bandwidth of the response to this force is proportional to 1/Q (where Q is the “quality factor” of the natural resonance peak), while the force sensitivity of the measurement is proportional to the Q of the natural resonance peak. Because, in many imaging applications, the bandwidth is the primary limiting factor of scan rate, the Q is designed to be low to allow for increased imaging speeds. However, reducing the Q of the cantilever correspondingly reduces force detection sensitivity, which thereby introduces noise into the AFM image.
A further contributing factor to less than optimal scan rates in cyclical mode operation is the fact that the amplitude error signal has a maximum magnitude. Over certain topographical features, a scanning AFM tip will pass over a dropping edge. When this occurs, the oscillation amplitude of the cantilever will increase to the free-air amplitude, which is not limited by tapping on the surface. The error signal of the control loop is then the difference between the free-air amplitude and the set point amplitude. In this instance, the error signal is at a maximum and will not increase with a further increase in the distance of the tip from the sample surface. The topography map will be distorted correspondingly.
Finally, the maximum gain of the control loop in cyclical mode is limited by phase shifts, thus further limiting the loop bandwidth. In view of these drawbacks, the Z position measurement for an atomic force microscope is typically characterized as being slew rate limited by the product of the maximum error signal and the maximum gain.
As a result, AFM technology posed a challenging problem if the scan rate in cyclical mode was to be increased significantly. One general solution proposed by Mertz et al. (Mertz, Marti, and Mlynek, “Regulation of a microcantilever response by force feedback,” Appl. Phys. Lett. 62 (19) at 2344–6 (1993)) (hereinafter “Mertz”), but not directed to existing cyclical mode AFMs, included a method for decreasing the effective Q of a cantilever while preserving the sensitivity of the natural resonance. In this method, a feedback loop is applied to the cantilever resonance driver such that the amplitude of the driver to the cantilever is modified based on the measured response of the cantilever. This technique serves to modify the effective Q of the resonating cantilever and will be referred to hereinafter as “active damping.” Mertz accomplished active damping by thermally exciting the cantilever by first coating the cantilever with a metal layer that had different thermal expansion properties than the cantilever beam itself. Then, in response to the feedback signals, Mertz modulated a laser incident on the cantilever, so as to apply a modified driving force.
When active damping is applied to the Mertz structure, mechanical resonances other than that of the cantilever are excited, and the gain of the active damping feedback cannot be increased enough to significantly modify the effective cantilever Q. Further, the Mertz design is prohibitively inflexible for systems contemplated by the present invention due to the fact that, among other things, the modulating laser only deflects the cantilever in one direction. This introduces a frequency doubling effect that must be accounted for to process the output. Overall, the Mertz system is complex and produces marginally reliable measurements at undesirably slow speeds.
In previous embodiments of the invention, an AFM with a Z position actuator and a self-actuated Z position cantilever (both operable in cyclical mode and contact mode), was implemented with appropriately nested feedback control circuitry to achieve high-speed imaging and accurate Z position measurements. The feedback signals applied to each of the actuators are independently monitored to indicate the topography of the sample surface, depending upon the scan rate and sample topography. Further, the feedback system can modify the effective Q of a resonating cantilever without exciting mechanical resonance's other than that of the cantilever. As a result, the system can optimize the Z-position bandwidth of the cantilever response to maximize scanning/imaging speeds, yet preserve instrument sensitivity.
Notably, however, the AFM cantilever is typically a consumable part of the system. The AFM cantilever tip wears out during the course of normal usage and must be frequently replaced. Each time a new AFM cantilever is introduced to the system, the driving oscillator must be adjusted to the natural resonance of the cantilever. In the previous embodiments of the Q modifying circuit, the cantilever is driven not only by the oscillator, but also by a filtered function of its own deflection. For each new cantilever, the transfer function of the Q modifying filter must be adjusted to optimize the response of the cantilever. This adjustment can be difficult to automate and typically requires either extensive computer processing or the intervention of an expert user.